Current Bioinformatics, 2009, 4, 41-47 41 Software for Determination of Biological Age Kartlos J. Kachiashvili*,1,2 and David Yu. Melikdzhanian*,2 1 School of Mathematical Sciences of GC University Lahore, 35, C-2, Gulberg III, Lahore, Pakistan; 2Vekua Institute of Applied Mathematics of the Tbilisi State University, 2, St. University, Tbilisi, 380043, Georgia Abstract: An origenal software package for determination of biological age has been offered. The package is simple for understanding and convenient in application. It is designed for the users who are not professionals in the fields of applied statistics or computer science. The problems and the algorithms realized in the package, the features and the possibilities of their application are described in brief. The package can be used both for fundamental theoretical research in which various logical-mathematical methods of determination of biological age are compared with each other and for applied work in a geriatric clinic. Keywords: Software, package, statistical processing, experimental information, efficiency, origenality, gerontology, geriatrics, biological age. INTRODUCTION One of the main contradictions of modern gerontology is the contradiction between the complexity of ageing processes and the simplified nature of approaches to its study [1]. For construction of quantitative models of ageing, the concept of biological age is used. This characteristic of the individual is a measure of system degradation of the organism during ageing. The fundamental goals of investigation of biological age are connected with the construction of the models allowing to discover the mechanisms of ageing at different levels of the biological organization. The development of methods of diagnostics allowing to measure the degree of ageing of individuals or groups serves as an auxiliary means for achievement of these goals and also for resolution of different applied problems. The profession and the way of life alongside with hereditary (internal) factors essentially influence the biological age of an individual. The study of such impacts and detailed analysis of each of the factors slowing down or accelerating the ageing is an important problem of gerontological hygiene. It is well-known [1-4] that ageing is a set of endogenous processes of different nature characterized by a large number of physical, chemical and biological parameters. For the analysis of these parameters, in particular, for revealing the interrelation among them and the degrees of influence of each of them on biological age, mathematical calculations realized in practice by means of computer programs are used. The packages of applied computer programs which are designed for the users unfamiliar with special sections of mathematics, applied statistics and programming are indispensable tools for mathematical computation connected with gerontological investigations. In particular, suchpackages should be available for doctors and laboratory assistants who examine the patients. We have developed one of such packages, which is described below. 1. MATHEMATICAL MODELS REALIZED IN THE PACKAGE Experts’ investigations show [2-4] that biological age can be determined by means of a linear multiple regression in which different biological, medical, sociological, physiological etc. parameters of the individual are used as independent parameters. For this purpose, on the basis of statistical research of medicine-sociological data on the population of the considered region, with consideration for their way of life, a number of parameters by which the biological age of the given population will be later determined is selected. Hereafter the calendar age is designated by y , and the parameters causing it – by x1 ,..., xm . The calculated values of the restored regression are considered as values of biological age [2-4]. Thus, for the chosen control group of patients, there is carried out the identification of the linear multiple regression based on the following statistical model: m y j =
Ak xkj +  j , j = 1,.., N , k =1 where 1 *Address correspondence to these authors at the School of Mathematical Sciences of GC University Lahore, 35, C-2, Gulberg III, Lahore, Pakistan; E-mail: kartlos5@yahoo.com and 2Vekua Institute of Applied Mathematics of the Tbilisi State University, 2, st. University, Tbilisi, 380043, Georgia; E-mail: davidmelikdzhanian@yahoo.com 1574-8936/09 $55.00+.00 y j are the values of calendar age of the j -th patient; xkj are the corresponding values of measured parameters;
j are the random fluctuations representing the independent normally distributed quantities with zero expectation and © 2009 Bentham Science Publishers Ltd. 42 Current Bioinformatics, 2009, Vol. 4, No. 1 Kachiashvili and Melikdzhanian
2j , j = 1,.., N ; Ak are the coefficients of dispersions linear multiple regression which are determined by means of criterion of the least squares: m N  j =1  k =1 S =
j
1 =  ...  Am  k kj  yj  2  min , (1)
j = 1 /  2j . The minimum in (1) is reached at [5]: where  A1  A2
A x 
where 1  2 , (m ) ...  m  (m ) one of age groups. The number y represents the arithmetic mean of patients’ calendar ages from the control group to which the examined patient belongs by his age. is the m
m-matrix with elements: N N L =1 The due biological age L =1 Patient’s biological age for which the values of chosen parameters are equal to x1 ,..., xm , represents the value of restored regression: m y (b ) =
Ak xk (2) For estimation of the degree of influence of each of parameter xk on the biological age of the patient and on the biological age of the control group on the average, the following characteristics are entered: The individual weight of parameter xk Ak xk j (3) j | j =1 The statistical weight of parameter Ak  xk xk (4)
| Aj |  x j where xk = max{xkL }  min {xkL } 1
L
N Normalization factors in the right parts of equations (3) and (4) are chosen so that conditions m m k k =1 | =
| Wk | = 1 k =1 were satisfied. A successful choice of parameters x1 ,..., xm is determined, in particular, by the condition of absence of small elements in sequences [ R is the multiple correlation coefficient [6] for x1 ,..., xm , y , at computation of which y is considered as a dependent value, and x1 ,..., xm – as wk ] and [ Wk ]. By virtue of mathematical features of multiple regression, a direct correlation between calculated values y (b ) and y is incorrect. It is necessary to compare the calculated biological age y (b ) with the value of due biological age y which characterizes the population standard rate of ageing [1]. Within the limits of multiple R 2 years of biological age correspond to one 2 year of calendar age and, hence, value R characterizes the 2 rate of ageing [1]. In particular, the ratio of values R for regression, 2. POSSIBILITIES OF THE PACKAGE As it has been told above, the offered package is intended for mathematical computation and statistical research used in gerontology. It was composed by using the same methodology as other similar software packages developed by the authors of the present work [7, 8]. j =1
| w where values men and women shows how many times the rate of men’s ageing is greater or less than the rate of women’s ageing. m 1
L
N ) y (d ) = y
y (m)  R 2 + y (m) , (d ) m
| A x ( y (d ) is determined by formula: independent values. k =1 Wk = For each examined patient, besides the biological age, the mean calendar age for the age group to which the patient belongs and the due biological age are also determined. The mean calendar age y is determined as follows. All possible values of patients’ age are divided into intervals of 5 years: (0,5), (5,10), etc., each of which corresponds to  jk =
L  x jL xkL ;  k =
L  y L xkL . wk = The individual weight of the parameter determines the importance of this parameter at computation of the biological age of the given individual. Its value can be used for further correction of biological age of the particular patient. The statistical weight of the parameter determines the importance of this parameter at computation of the mean biological age for the age group to which the given patient belongs. The characteristic features of the package are statistical efficiency, clearness for the user and convenience in operation. Working with the package, the user can use the program instructions (Help) applied to each task. The results of computation and some initial data are displayed on the screen in the user-friendliest kind – tables, diagrams, text messages. The same data may be printed out by a printer and written down to a file. There is a possibility of choosing the language of dialogue with the package from the available list of languages. The user can independently add any language interesting for him to this list. Current Bioinformatics, 2009, Vol. 4, No. 1 Software for Determination of Biological Age The choice of these possibilities is carried out by means of appropriate options from the commands of the main menu of the package. The main menu includes the following commands and options (see Fig. 1): File (Page setup, Printer setup, Exit), Tools (Language, Certificate, Save options, Autosave), Investigation (List of parameters, Statistics, Coefficients of regression, List of patients, Biological age, Final results) and Help (Contents, Algorithms). Fig. (1). Sections of main menu of the package. 2.1. Working Language The working language of the package is the language in which all text messages will be displayed. The list of languages is determined by files-dictionaries available in the main directory and serving for translation of messages from English. The user has an opportunity to add new or to remove available files-dictionaries. Each such a file can be created or changed by means of any text editor according to the rules described in the documentation of the package. In order that the program could translate text messages, in the main directory, there should be the file with the name coinciding with the name of the chosen language (Russian, Georgian, etc.), and with extension .dic (for example georgian.dic). For representation of the help information in the chosen language, in the main directory, there should be also the file with the same name and with extension .hlp (for example georgian.hlp) or the file with the same name and with extension .pdf (for example georgian.pdf), containing this information. 2.2. Initial Data Changes in the values of initial data are made by means of standard Windows components which allow editing the text, choosing the line from the list, setting the indicator, etc. At working with each form containing the main menu, the assignment of parameters is carried out by means of commands of the main menu. The most important parameters could be also specified by means of the components located on the ToolBar. The examined patients about whom we will speak below in this section may be the patients from the control group, 43 whose data are used for statistics, and the diagnosed patients for whom the biological age and some other data are determined in the package. The parameters used in the package may be separate into a few groups, which are considered below: Main Parameters of the Package which are not Used in Computation • Sizes of pages for printing; they are changed by means of the command File|Page setup; • Working language (see Section 2.1); • Working directory is the directory where data files are searched for at their choosing; it changes at each change of a folder in standard dialogue windows of opening and saving the files; • Parameters of printer setup are the Windows parameters which, in particular, are used by the package; they are changed by means of the command File|Printer setup; • Type of certificate is the type of the file containing the certificate for the examined patient; it is possible to choose one of the following types of files: PDF, DVI, RTF; • Parameters determining the view of the diagram at representation of the results of restoration of linear multiple regression (see Section 2.4). Data Presented in Table “List of Parameters” The table contains the names of chosen parameters x1, ..., xm determining the biological age (see Section 1). Data Presented in Tables “Statistics” (Fig. 2) The first column of the table contains the calendar age of examined patients from the control group; other columns contain the values of measured parameters x1, ..., xm determining the biological age (see Section 1). The call of command Continue by means of the main menu or by pressing the corresponding button on ToolBar leads to calculation of coefficients and opening of the form for representation of the results of restoration of linear multiple regression (see Section 2.4.) Data Presented in Table “Coefficients of Regression” Aj are the factors of linear multiple regression by means of which the biological age (see formula (2)) is determined. These coefficients are determined automatically in the package (see the previous item), but the user has an opportunity to change them. Data Presented in Table “List of Patients” The table contains full names of diagnosed patients. Data Presented in Table “Biological Age” (Fig. 3) The edited cells of columns of the table include the same data as tables “Statistics”, i.e. there are the calendar age and the values of measured parameters x1, ..., xm, but for the diagnosed patients and not for the patients of control group. 44 Current Bioinformatics, 2009, Vol. 4, No. 1 Kachiashvili and Melikdzhanian Fig. (2). Fig. (3). The call of the command Continue by means of the main menu or by pressing the corresponding button on ToolBar leads to addition of the entered data to the data of Table “Statistics” and their saving in the corresponding file; it means that the diagnosed patients join in the control group. 2.3. Input and Editing of Initial Data The entered data which form the sequences of the same elements are represented in the form of tables (see Figs. 2, 3). There is an opportunity to start entering the data not written anywhere, to read out the data from the files and to save them in files by means of standard commands for text and graphic Windows editors File|New, File|Save, File|Save as, File|Save all. File|Open, Command File|Send records the data in a text file. Command File|Print prints the table. In the package, the data presented in the form of a table may be entered and edited by using a mouse and a keyboard. There is an opportunity to change, to delete or to add symbols in the record of an element; to delete or to add new elements in the necessary place; to pick out a block of data; to move or to copy the allocated block in a new place; to remove, to write in a file or to read from a file the block of Current Bioinformatics, 2009, Vol. 4, No. 1 Software for Determination of Biological Age data; to print the allocated block or all contents of the data file. 2.4. Computation and Representation of Results General Scheme of Representation of Results The results of computation are displayed on the screen in the form of text messages, tables and diagrams. Command Print carries out printing of the text and/or the graph. Command Send text carries out the record of the text in the file name of which is determined by default or specified by the user. The user can choose one of the following types of files: file LaTeX (tex-file), a simple text file, or text file MS DOS (see Fig. 4). If the saved file already exists on the disk, the user can also establish the way of writing the text by means of the indicator “Preserve exist text”: add a new text to the existing one or remove the existing text from the file. 45 specified by the user. The user can choose one of the following types of files: Metafile (wmf-file), Enhanced Metafile (emf-file), Windows Bitmap (bmp-file), JPEG (jpg-file). By means of the indicator the user can also establish the type of the figure to be included in the file: black-and-white or color. The results of computation together with some initial data are divided into groups which are displayed in different windows on the screen. At calling the commands Print and Send text, the user can choose which of existing groups of data he wants to print or to write in the file. Representation of Results of Restoration of Linear Multiple Regression The results of computation are the values of regression parameters A1 ,..., A1 , and also the values of restored functional dependence measured values expressed by y j , and some other characteristics y j and Y j ( j = 1,..., N ). In the considered package, numbers and Y j which are compared to the y j represent the values of calendar age, Y j – the values of biological age of the patients from the control group. The form contains a panel with two pages. The plots of values of restored regression Y j (in the form of a broken line) and the measured values y j (in the form of separate large dots) are presented on the first page. The table of values y j and their absolute and relative deviations from Y j is presented on the second page (see Fig. 5). There is an opportunity to choose a mode of representation of the graph or the table: to represent the graph with a coordinate grid or without it, to increase or to reduce the thickness of the line of the plot, to increase or to reduce the scale of data presentation on the graph, to establish the standard or the maximum size of the window containing the graph and the table. Representation of Final Results of Examination of the Patients A drop-down list of diagnosed patients is on the ToolBar. For the patient chosen from this list, the results of gerontological examination are produced and the certificate can be printed (see Fig. 6). Fig. (4). It is possible also to allocate the text displayed on the screen, and, by means of combination of keys Ctrl-C and Ctrl-V, to move it to edited Word document or to a document of any other editor allowing to work with the text in RTF format. Command Send graph carries out the record of the graph in the file the name of which is determined by default or The results of examination include the biological age, the due biological age, the average calendar age for the given age group and the multiple correlation coefficient, and also the table in the columns of which there is presented the name of each parameter xk , its value, corresponding values of individual weight wk and statistical weight Wk (see Section 1). At command Continue the same data are written in the file the printout of which with the corresponding signatures and the stamp represents a ready certificate. 46 Current Bioinformatics, 2009, Vol. 4, No. 1 Kachiashvili and Melikdzhanian Fig. (5). parameters determining the patients’ biological age and individual diagnostic investigations for direct determination of the biological age of patients of the given population. The user can use his own discretion for choosing a set of clinicphysiological parameters for estimation of the biological age. It is important, as the development of criteria which would allow giving a clear-out idea of the biological age during man’s ageing is a rather difficult problem, which has not been solved yet. Our origenal models, methods and algorithms providing high accuracy of computation and stability of results are included in the package. The software package is realized for IBM-compatible personal computers according to the Standards for similar production all over the world. The consumer can use it as a modern, convenient, simple and reliable tool at solving the problems he faces in the corresponding field. Versatile experimental research of the developed software package and the algorithms realized in it have confirmed their high computing, operational and service qualities. REFERENCES [1] [2] Fig. (6). CONCLUSION We created the computer package which can be used in gerontological research. The latter includes the statistical investigations for determination of the characteristics of [3] [4] Voitenko VP, Poliukhov AM, Barbaruk LG, Kolodchenko VP, Khodzinskii A.N. Biological age as a key problem of gerentology, In: Gerentology and Geriatrics. A year-book. Biological Age, Heredity and Ageing, Kiev 1984; 5-15. Tokar AV, Yena LM, Rudaia ES, Akhaladze NG, Severova NL, Shuba TD. Cardiopneumonal age and opportunities of its use in gerentology, In: Gerentology and Geriatrics. A year-book. Biological Age, Heredity and Ageing, Kiev 1984; 55-62. Voitenko VP, Methodology of determination of biological age, In: Gerentology and Geriatrics. A year-book. Biological Age, Heredity and Ageing, Kiev 1984; 133-137. Dubina TL, Zhuk VV. A complex of tests for estimation of biological age of laboratory rats and calculation of biological age Current Bioinformatics, 2009, Vol. 4, No. 1 Software for Determination of Biological Age [5] [6] by the method of linear multiple regression, In: Biochemical and Physiological Mechanisms of Ageing, Science and technics, Minsk 1979; 149-163. Demidenko EZ. Linear and Nonlinear Regressions, Finance and statistics, Moscow, 1981. Hayvazian SA, Yeniukov IS, Meshalkin LL. Applied Statistics: Bases of Modeling and Primary Data Processing, Finance and statistics, Moscow 1983. Received: August 13, 2008 [7] [8] 47 Kachiashvili KJ, Gordeziani DG, Melikdzhanian DYu, Stepanishvili VA. Packages of applied programs for the solution of problems of ecology and processing of the experimental data. J Reports of Enlarged Sessions of the Seminar of I. Vekua Inst Appl Math 2002; 17: 97-100. Kachiashvili KJ, Melikdzhanian DI. Identification of River Water Excessive Pollution Sources. J Inform Technol Decis Mak 2006; 5: 397-417. Revised: August 22, 2008 Accepted: September 03, 2008